Add the following rational expressions. $\dfrac{-m+6}{m^2-16}+\dfrac{2m-2}{m^2-16}=$
Answer: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{-m+6}{m^2-16}+\dfrac{2m-2}{m^2-16} \\\\ &=\dfrac{(-m+6)+(2m-2)}{m^2-16} \\\\ &=\dfrac{-m+6+2m-2}{m^2-16} \\\\ &=\dfrac{m+4}{m^2-16} \end{aligned}$ In conclusion, $\dfrac{-m+6}{m^2-16}+\dfrac{2m-2}{m^2-16}=\dfrac{m+4}{m^2-16}$